Fifth year TA line or a paid summer internship when I have two chapters left Career

Internship, if you genuinely mean non-academic. Four sections of teaching is 20 hours a week of work that appears on your CV as one line nobody outside a university will read. Twelve weeks in an industry research group gives you a reference who is not your advisor, a project you can describe in an interview without translating, and a realistic sense of whether you want that world. The catch is that summer is often the only block of uninterrupted analysis time you get, so ask yourself honestly whether your fifth year is a finishing year or a stalling year.

Teaching four sections while finishing is not neutral, it is actively negative. I taught three in my last year and lost every morning to grading guilt. If you stay, negotiate down to two sections and see whether the department blinks.

One thing nobody mentions: tell your advisor about the internship as an opportunity rather than a question. Advisors who would say no to "may I" often say "congratulations" to "I've been offered this and I plan to take it, here's my writing plan for the autumn."

Ask one boring question before deciding: does the TA line come with a tuition waiver and health cover that the internship does not? People compare gross pay and forget that the assistantship is often quietly worth another 15 to 20 thousand in things you would otherwise pay for. If the internship is cash only and you lose enrolment status for the summer, the numbers can flip completely.

I chose the TA line in the same spot and finished on time. It is genuinely easier to write when your whole life is inside one building. I do not regret it, but I also stayed in academia, which sounds like it is not your plan.